- #1
Alexx1
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Can someone help me with this integral?
e^(-1/x)
e^(-1/x)
If the problem were [itex]\int e^u du[/itex], but it isn't and there is no good way to change it to that form.CFDFEAGURU said:Just follow the rules for exponential integration.
[tex]\int[/tex] [tex]e^{u}[/tex] du = [tex]e^{u}[/tex] + C
Thanks
Matt
The integral of e^(-1/x) is a special function called the exponential integral, symbolized as Ei(x). It is defined as the integral from 0 to x of e^(-t)/t dt.
The integral of e^(-1/x) has various applications in mathematics, physics, and engineering. It is used in the solution of differential equations, in the calculation of the area under an exponential curve, and in the evaluation of some probability distributions.
No, the integral of e^(-1/x) is not a continuous function. It is only continuous for positive values of x. For x = 0, the integral diverges.
No, the integral of e^(-1/x) cannot be expressed in terms of elementary functions. It is a special function that does not have a closed-form expression.
The integral of e^(-1/x) is closely related to the gamma function. In fact, it can be expressed in terms of the gamma function as Ei(x) = -Γ(0,x). This relationship is useful in evaluating the integral for different values of x.